Steady state fluid response in fractured rock: A boundary element solution for a coupled, discrete fracture continuum model

Abstract

A discrete fracture representation of a highly fractured groundwater aquifer is inappropriate as a modeling approach since the location of all fractures can never be explicitly specified. However, the alternative of exclusively employing a continuum description of the medium then neglects any geologic information that exists with regard to the location of specific fractures in such formations. In order to take better advantage of geologic information in highly fractured aquifers a model is proposed which couples the discrete fracture and continuum conceptualizations. In regions where discrete fractures are designated, an effecient means of computing the steady state fluid responses is formulated with the use of the boundary element method. This allows the consideration of highly complex fracture geometries, since fluid responses in the porous rock are described with a set of linear equations written only in terms of the hydraulic head and fluid mass flux at the boundaries the porous rock shares with the fractures. One‐dimensional equations of fluid movement in the fractures written in terms of the same variables make coupling of the two systems straight forward. In this technique, discretization only along the fractures is required. Thus the internal discretization of the host rock that would be characteristic in the use of finite difference and finite element methods is alleviated. At the boundary of the region where specific fractures are identified, a continuum conceptualization is coupled to the discrete fracture model. Steady state fluid responses in the continuum domain are defined using a semianalytic technique which is based on the discretization of Green's third identity. The resulting coupled model allows the discrete fracture and continuum conceptualizations to be employed in the modeling of those areas where they are judged to be most appropriate, based on the availability of physical information.